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TRS Standard pair #487069296
details
property
value
status
complete
benchmark
ma96.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.098381 seconds
cpu usage
0.04957
user time
0.037147
system time
0.012423
max virtual memory
113188.0
max residence set size
6272.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 1: and(false(),false()) -> false() 2: and(true(),false()) -> false() 3: and(false(),true()) -> false() 4: and(true(),true()) -> true() 5: eq(nil(),nil()) -> true() 6: eq(cons(T,L),nil()) -> false() 7: eq(nil(),cons(T,L)) -> false() 8: eq(cons(T,L),cons(Tp,Lp)) -> and(eq(T,Tp),eq(L,Lp)) 9: eq(var(L),var(Lp)) -> eq(L,Lp) 10: eq(var(L),apply(T,S)) -> false() 11: eq(var(L),lambda(X,T)) -> false() 12: eq(apply(T,S),var(L)) -> false() 13: eq(apply(T,S),apply(Tp,Sp)) -> and(eq(T,Tp),eq(S,Sp)) 14: eq(apply(T,S),lambda(X,Tp)) -> false() 15: eq(lambda(X,T),var(L)) -> false() 16: eq(lambda(X,T),apply(Tp,Sp)) -> false() 17: eq(lambda(X,T),lambda(Xp,Tp)) -> and(eq(T,Tp),eq(X,Xp)) 18: if(true(),var(K),var(L)) -> var(K) 19: if(false(),var(K),var(L)) -> var(L) 20: ren(var(L),var(K),var(Lp)) -> if(eq(L,Lp),var(K),var(Lp)) 21: ren(X,Y,apply(T,S)) -> apply(ren(X,Y,T),ren(X,Y,S)) 22: ren(X,Y,lambda(Z,T)) -> lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil())))),ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil())))),T))) Number of strict rules: 22 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #eq(apply(T,S),apply(Tp,Sp)) -> #and(eq(T,Tp),eq(S,Sp)) #2: #eq(apply(T,S),apply(Tp,Sp)) -> #eq(T,Tp) #3: #eq(apply(T,S),apply(Tp,Sp)) -> #eq(S,Sp) #4: #eq(var(L),var(Lp)) -> #eq(L,Lp) #5: #ren(var(L),var(K),var(Lp)) -> #if(eq(L,Lp),var(K),var(Lp)) #6: #ren(var(L),var(K),var(Lp)) -> #eq(L,Lp) #7: #ren(X,Y,lambda(Z,T)) -> #ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil())))),T)) #8: #ren(X,Y,lambda(Z,T)) -> #ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil())))),T) #9: #eq(lambda(X,T),lambda(Xp,Tp)) -> #and(eq(T,Tp),eq(X,Xp)) #10: #eq(lambda(X,T),lambda(Xp,Tp)) -> #eq(T,Tp) #11: #eq(lambda(X,T),lambda(Xp,Tp)) -> #eq(X,Xp) #12: #ren(X,Y,apply(T,S)) -> #ren(X,Y,T) #13: #ren(X,Y,apply(T,S)) -> #ren(X,Y,S) #14: #eq(cons(T,L),cons(Tp,Lp)) -> #and(eq(T,Tp),eq(L,Lp)) #15: #eq(cons(T,L),cons(Tp,Lp)) -> #eq(T,Tp) #16: #eq(cons(T,L),cons(Tp,Lp)) -> #eq(L,Lp) Number of SCCs: 2, DPs: 11 SCC { #7 #8 #12 #13 } POLO(Sum)... succeeded. apply w: x1 + x2 + 1 ren w: x3 and w: x2 + 3 eq w: x2 + 47562 lambda w: x2 + 2 false w: 47568 true w: 47564 #eq w: 0 if w: x3 nil w: 1 #ren w: x2 + x3 cons w: x1 + x2 + 1 #if w: 0 var w: 1 #and w: 0 USABLE RULES: { 18..22 } Removed DPs: #7 #8 #12 #13 Number of SCCs: 1, DPs: 7 SCC { #2..4 #10 #11 #15 #16 } POLO(Sum)... succeeded. apply w: x1 + x2 + 1 ren w: x3 and w: x2 + 2 eq w: x2 + 35495 lambda w: x1 + x2 + 1 false w: 35500 true w: 35497 #eq w: x1 + x2 if w: x3 nil w: 1 #ren w: 0 cons w: x1 + x2 + 1 #if w: 0 var w: x1 + 1 #and w: 0 USABLE RULES: { 19 } Removed DPs: #2..4 #10 #11 #15 #16 Number of SCCs: 0, DPs: 0
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